On the generalized convolution with a weight function for the Fourier cosine and the inverse Kontorovich-Lebedev integral transformations. (English) Zbl 1142.44007

Tuan, Trinh

Nonlinear Funct. Anal. Appl. 12, No. 2, 325-341 (2007).

The author introduces the generalized convolution with the weight function \(\gamma(y)=1/(y\sinh(\pi y))\) for the Fourier cosine integral transform \((F_c)\) and the inverse Kontorovich-Lebedev integral transform \((K^{-1})\). The integral transform \((F_c)\) and \((K^{-1})\) appear in the factorization identity of this convolution, therefore these results totally differ from that for the generalized convolutions published in previous works. The new convolution is applied to solve two systems of integral equations.

Reviewer: Alexandr L. Brodskij (Severodonetsk)

MSC:

44A35	Convolution as an integral transform
44A15	Special integral transforms (Legendre, Hilbert, etc.)
42A38	Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
45F15	Systems of singular linear integral equations

Keywords:

generalized convolution; Fourier cosine integral transform; inverse Kontorovich-Lebedev integral transform; systems of integral equations